Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Ab initio investigation of benzene clusters: molecular tailoring approach

An exhaustive study on the clusters of benzene (Bz)(n), n = 2-8, at MP2/6-31++G(??) level of theory is reported. The relative strengths of CH-π and π-π interactions in these aggregates are examined, which eventually govern the pattern of cluster formation. A linear scaling method, viz., molecular tailoring approach (MTA), is efficiently employed for studying the energetics and growth patterns of benzene clusters consisting up to eight benzene (Bz) units. Accuracy of MTA-based calculations is appraised by performing the corresponding standard calculations wherever possible, i.e., up to tetramers. For benzene tetramers, the error introduced in energy is of the order of 0.1 mH (～0.06 kcal/mol). Although for higher clusters the error may build up, further corrections based on many-body interaction energy analysis substantially reduce the error in the MTA-estimate. This is demonstrated for a prototypical case of benzene hexamer. A systematic way of building up a cluster of n monomers (n-mer) which employs molecular electrostatic potential of an (n-1)-mer is illustrated. The trends obtained using MTA method are essentially identical to those of the standard methods in terms of structure and energy. In summary, this study clearly brings out the possibility of effecting such large calculations, which are not possible conventionally, by the use of MTA without a significant loss of accuracy.     

A theoretical study on structural, spectroscopic and energetic properties of acetamide clusters [CH3CONH2] (n=1-15)

Insights into the formation of hydrogen bonded clusters are of outstanding importance and quantum chemical calculations play a pivotal role in achieving this understanding. Structure and energetic comparison of linear, circular and standard forms of (acetamide)(n) clusters (n = 1-15) at the B3LYP/D95** level of theory including empirical dispersion correction reveals significant cooperativity of hydrogen bonding and size dependent structural preference. A substantial amount of impact of BSSE is observed in these calculations as the cluster size increases irrespective of the kind of arrangement. The interaction energy per monomer increases from dimer to 15mer by 90% in the case of the circular arrangement, by 76% in the case of the linear arrangement and by 34% in the case of the standard arrangement respectively. The cooperativity in hydrogen bonding is also manifested by a regular decrease in average OH and C-N bond distances, while average C=O and N-H bond lengths increase with increasing cluster size. Atoms-In-Molecules (AIM) analysis is used to characterize the nature of hydrogen bonding between the acetamide molecules in the cluster on the basis of electron density (ρ) values obtained at the bond critical point. An analysis of N-H bond stretching frequencies as a function of the cluster size shows a marked red shift as the cluster size increases from 1 to 15.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.     

High precision delta(17)O isotope measurements of oxygen from silicates and other oxides: method and applications

The use of infrared laser-assisted fluorination to release oxygen from milligram quantities of silicates or other oxide mineral grains is a well-established technique. However, relatively few studies have reported the optimisation of this procedure for oxygen-17 isotope measurements. We describe here details of an analytical system using infrared (10 μm) laser-assisted fluorination, in conjunction with a dual inlet mass spectrometer of high resolving power ( approximately 250) to provide (17)O and (18)O oxygen isotope measurements from 0.5-2 mg of silicates or other oxide mineral grains. Respective precisions (1) of typically 0.08 and 0.04 per thousand are obtained for the complete analytical procedure. Departures from the mass-dependent oxygen isotope fractionation line are quantified by Delta(17)O; our precision (1) of such measurements on individual samples is shown to be +/-0.024 per thousand. In turn, this permits the offset between parallel, mass-dependent fractionation lines to be characterised to substantially greater precision than has been possible hitherto. Application of this system to investigate the (17)O versus (18)O relationship for numerous terrestrial whole-rock and mineral samples, of diverse geological origins and age, indicates that the complete data set may be described by a single, mass-dependent fractionation line of slope 0.5244+/- 0.00038 (standard error). Copyright 1999 John Wiley & Sons, Ltd.     

Test of bell’s inequality using the one-atom micromaser

We examine a local realist bound in the case of a one-atom micromaser. It is shown that such a bound is violated using a simplified treatment of the micromaser. We consider the effect of dissipation in a proposed experiment with the real micromaser. It is seen that the magnitude of violation of a Bell-type inequality depends significantly on the cavity parameters.     

First principles study and database analyses of structural preferences for sodium ion (Na+) solvation and coordination

Extensive computations were performed on aqueous clusters of monovalent sodium cation [Na⁺(H₂O) _n ; (n = 1–20)] using MP2/cc-pVTZ and density functional theory. The structure, energy, and coordination number (CN) preference of a large number of competing conformations of different complexes have been explored. For complexes up to n = 12, the CN 4 is most preferred while 5, 6 CNs are favored in case of larger complexes containing up to 20 water molecules. These results are in very good agreement with experimental observations. The strength of hydrogen bonding among the waters coordinated to the Na⁺ ion is found to play a major role in the stability of the complexes. The varying preferences for CN of Na⁺ ion were explored by screening two important databases: Protein Databank and Cambridge Structural Database. A linear correlation is observed between the M (Metal)–O distance and the charge on metal ion in complex with the increase in CN of metal ion.     

Analyzing coordination preferences of Mg2+ complexes: insights from computational and database study

Solvation of metal cations has attracted substantial interest on account of its functional importance in biological systems. In the present study, we undertake a comprehensive analysis of hydrated complexes of Mg²⁺ with up to 20 water molecules using MP2/cc-pVTZ and density functional theory (DFT) calculations. The effect of first, second, and higher solvation shells on magnesium coordination has been systematically analyzed by considering Mg²⁺(H₂O) _n complexes. Numerous competing conformations for each of the metal ion complexes have been explored and the minima structures obtained were further analyzed. The study probes the relative preferences among various coordination numbers and unambiguously establishes that coordination number 6 is the most optimal choice. The relative abundance of Mg²⁺ ion and its coordination with water and other ligands has been analyzed in the Protein Data Bank and Cambridge Structural Database. It is noted that the M–O distance and charge transfer to metal ion increase as the number of solvating water molecules increases. The computational studies are in excellent agreement with the experimental observations, and provide support to multiple coordinate site preferences for Mg²⁺.     

On the beam propagation through active media

An analytical iterative procedure has been established to determine the amplitude of a laser beam propagating through an active medium. The treatment is valid for both homogeneous and inhomogeneous broadening, and for arbitrary inhomogeneities of the parameters characterizing the active medium, namely, the refractive index, the small-signal gain and the saturation intensity. After a supplementary approximation, a thin-sheet gain approach is derived from the first iteration. The formalism enables us to provide analytical criteria for evaluating both the accuracy of each iteration and the propagation distances for which the thin-sheet solution can be used. This revised version was published online in November 2006 with corrections to the Cover Date.